# Martin

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 Sep9 comment Formula for surface measure of spherical cap on $S^n$. In the section 'hyperspherical cap', the wikipedia article gives a formula for the surface in terms of regularized incomplete beta functions. I wonder whether a single integral formula like for the volume, at the beginning of the same section, does exist. Sep8 comment Formula for surface measure of spherical cap on $S^n$. I am specifically looking for formulas nicer than there. Apr5 comment Boundedness of a Solution Operator @user17904: You need to show that for Sobolev space $H$ of sufficient regularity the trace from $H$ to $L^2(\partial\Omega)$ has closed range. Than a bounded right-inverse exists by functional analysis. Typically, you can prove surjectivity, say, by partition of unity, smoothing and an explicit construction. Mar7 comment pseudoinverse under change of norm I have completely rewritten the question. Mar4 comment An variation of “Lk” in simplicial complexes @StefanH.: Yes, thanks. Feb13 comment How can not-equals be expressed as an inequality for a linear programming model It is intutive it does not work, because polyhedrons are convex and closed, while not-equals correspond to non-convex open regions. Jan29 comment Approaches to integrate $\int_0^1 \frac{x}{\sqrt{a+bx+cx^2}} dx$ Thanks, that got me on the right track. Jan27 comment If A $\subset S^n$ has spherical diameter < $\pi$, then $S^n - A$ contains a closed semisphere. The original statement was blatantly wrong. I have editted the question into what I actually meant. Dec19 comment Distinction between 'adjoint' and 'formal adjoint' These lines on Wikipedia only describe the construction for a differential operator. I have been concerned about general operators and their formal adjoints. Nov2 comment Solid angle between vectors in n-dimensional space Your second formula is quite awkward, because you apply arctan against a vector. Jul18 comment Proof by Induction $n^2+n$ is even You know you don't need induction, do you? Jul11 comment Minimizer of $p$-average of distances to points $x_1,\dots,x_n$ @ChristianBlatter: A name, like some exotic mean, would be helpful, of course. Jul11 comment Minimizer of $p$-average of distances to points $x_1,\dots,x_n$ @Paul: Yes, by definition. The vector $D$ is just a formal device. Apr7 comment Antisymmetric functions in higher dimensions Okay, maybe a nice definition of signed permuation of coordinates is a permuation matrix times a ${-1,1}$-diagonal matrix, and the signum is the determinant of that transform. Apr7 comment Antisymmetric functions in higher dimensions That's interesting. Your functions are smooth, are they? And could you please define what a signed permuation and its signum mean? Mar18 comment How should I understand “$A$ unless $B$”? That post is nicely written. Thanks! Mar13 comment Derivative in complex analysis @anon: I am curious and my complex analysis is rusty, too. Why is $f$ constant? Mar7 comment Which formula do I use to integrate $\int {\sqrt{x^2 + 81} \over 2} \,dx$ In your final expression, the variable $x$ appears outside the integral, without any proper definition there. You should change this notation. Mar1 comment First-order derivatives in differential forms calculus Because that is the way the Lie differential is defined. Feb22 comment What is the theory of non-linear forms (as contrasted to the theory of differential forms)? I guess these non-linear forms are taken from David Bachmann's book "A Geometric Approach to Differential Forms", aren't they?